The broad, long-term objectives of this research are the developments of semiparametric regression models and associated inference procedures for the statistical analysis of censored data commonly encountered in biomedical investigations. The specific aims of the next project period include: (1) to explore a broad class of semiparametric regression models, called generalized Cox models, which extends the Cox regression model to accommodate various non-proportional hazards structures;(2) to construct efficient estimators for a class of mixture cure models which combines a binary regression model for the cure probability with a generalized Cox model for the failure times of the uncured individuals;(3) to investigate a class of joint models for repeated measures and event times which formulates the distribution of discrete or continuous repeated measures with the generalized linear mixed model and which formulates the event times with the generalized Cox model with random effects;(4) to study a class of joint models for recurrent and terminal events which formulates the event times through generalized Cox models with random effects;(5) to derive efficient methods for estimating the effects of haplotypes on the age of onset of a disease in genetic association studies with the case-cohort or nested case-control design;(6) to pursue variable selection strategies for generalized Cox models and accelerated failure time models. All these problems are motivated by the principal investigator's applied research experiences, and are highly relevant to a wide variety of biomedical studies. The proposed solutions are based on likelihood and other sound statistical principles. The large-sample properties of the proposed estimators will be established rigorously via modern empirical process theory and semiparametric efficiency theory. Efficient and reliable numerical algorithms will be developed to implement the inference procedures. The operating characteristics of the proposed methods will be evaluated through extensive simulation studies. Applications to major clinical and epidemiological studies will be provided. Relevant software will be made available to the general public. This research will not only significantly advances the fields of survival analysis and longitudinal data analysis, but will also provide valuable new tools to biomedical researchers.